Constructions of bent functions from two known bent functions

A (1, -1)-matrix will be called a bent type matrix if each row and each column are bent sequences. A similar description can be found in Carlisle M. Adams and Stafford E. Tavares, Generating and counting binary sequences, IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 1170-1173, 1990 in which the authors use the properties of bent type matrices to construct a class of bent functions. In this paper we give a general method to construct bent type matrices and show that the bent sequence obtained from a bent type matrix is a generalized result of the Kronecker product of two known bent sequences. Also using two known bent sequences of length 22k-2 we can construct 2k-2 bent sequences of length 22k more than in the ordinary construction, which gives construct 10 bent sequences of length 22k from two known bent sequences of length length 22k-2

The kth-order nonhomomorphicity of S-boxes

Nonhomomorphicity is a new nonlinearity criterion of a mapping or S-box used in a private key encryption algorithm. An important advantage of nonhomomorphicity over other nonlinearity criteria is that the value of nonhomomorphicity is easy to estimate by the use of a fast statistical method. Due to the Law of Large Numbers, such a statistical method is highly reliable. Major contributions of this paper are (1) to explicitly express the nonhomomorphicity by other nonlinear characteristics, (2) to identify tight upper and lower bounds on nonhomomorphicity, and (3) to find the mean of nonhomomorphicity over all the S-boxes with the same size. It is hoped that these results on nonhomomorphicity facilitate the analysis and design of S-boxes

Nonlinearity and propagation characteristics of balanced boolean functions

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable by any previously known construction method. We also present methods for constructing balanced Boolean functions that are highly nonlinear and satisfy the strict avalanche criterion (SAC). Furthermore we present methods for constructing highly nonlinear balanced Boolean functions satisfying the propagation criterion with respect to all but one or three vectors. A technique is developed to transform the vectors where the propagation criterion is not satisfied in such a way that the functions constructed satisfy the propagation criterion of high degree while preserving the balancedness and nonlinearity of the functions. The algebraic degrees of functions constructed are also discussed, together with examples illustrating the various constructions

A Bridge Between Two Worlds: a Cultural Interpretation of Dragonwings

Living in the dual worlds of his life as a Chinese American and in places such as Chinatown, Laurence Yep felt that he was culturally alienated and that he did not have a culture of his own. With the driving wish to find out about Chinese culture―his culture, he finished his best known novel Dragonwings after six years of research on Chinese culture. Based on the true story of Fung Joe Guey, a Chinese American who built and flew an airplane in the Oakland hills in 1909, Dragonwings tells the story of Moon Shadow, who comes to San Francisco to join his unknown father, Windrider, who cherishes the dream of flying. To pursue the dream, Moon Shadow and his father have to move out of Chinatown. After enduring a sea of misunderstanding, cruelty and poverty, Windrider finally realizes his flying dream with the support and aid of his beloved son and his fellowmen, as well as his American friends. Trying to show the process from misinterpretation and misunderstanding to mutual understanding and the possibilities of cultural exchange and cultural fusion between two different cultures, we will discuss how the Chinese culture is rediscovered by a Chinese American and how cultural misunderstanding leads to an unbalanced world and how tolerance and understanding restore the world into a harmonious one. This paper attempts to demonstrate, through the analysis of Dragonwings, the author’s exploration of Chinese culture, cultural exchange and human nature transcending cultural differences. Key words: Dragonwings, Laurence Yep, cultural exchange Abstrait: En vivant dans le monde dual de sa vie comme Américain chinois et aux endroits comme la Cité chinoise, Laurence Yep trouve qu’il était aliéné culturellement et qu’il n’avait pas de culture de sa ville. Avec l’espoir violent à découvrir la culture chinoise----sa culture, il a achevé son roman bien connu Dragon-ailes après une recherche de six années sur la culture chinoise. Basé sur l’histoire vraie de Fung Joe Guey , un Américain Chinois qui a fabriqué et manié un avion dans les Montagnes Oakland en 1909, Dragon-ailes raconte le conte de Ombre de lune, qui vient à San Francisco pour rejoindre son père inconnu , Windrider, qui a le rêve de voler .Poursuivant le rêve, Ombre Lunaire et son père sont obligés de bouger de la Cité chinoise. Après avoir enduré une mer d’incompréhension , de cruauté et de pauvreté, Windrider a finalement réalizé son rêve de voler avec l’aide de son fils et ses compagnons, ainsi que ses amis américains. Essayant de montrer le processus de malinterprétation et de incompréhension à compréhension mutuelle et les possibilités d’échange et de fusion culturels entre deux cultures différentes, nous discuterons comment la culture chinoise est redécouverte par un Américian chinois et comment l’incompréhension culturelle conduit à un monde inégal et comment la tolérance et la compréhension reconstruisent le monde à celui d’harmonique. Ce papier tente de démontrer , à travers l’analyse de Dragon-ailes , l’exploration de l’auteur de la culture chinoise , de l’échange culturel et des différences transcendantes naturelles de la nature humaine. Mots clefs: Dragon-ailes, Laurence Yep, échange culture

On Cheating Immune Secret Sharing

The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2^n ∑ _c=1...n ∑ _α ∈V n ρ _c,α , denoted by øverlineρ , satisfies øverlineρ ≥ \frac12 , and the equality holds if and only if ρ _c,α satisfies ρ _c,α = \frac12 for every cheating vector δ _c and every original vector α . In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing

The Generalized XOR Lemma

Abstract The XOR Lemma states that a mapping is regular or balanced if and only if all the linear combinations of the component functions of the mapping are balanced Boolean functions. The main contribution of this paper is to extend the XOR Lemma to more general cases where a mapping may not be necessarily regular. The extended XOR Lemma has applications in the design of substitution boxes or S-boxes used in secret key ciphers. It also has applications in the design of stream ciphers as well as one-way hash functions. Of independent interest is a new concept introduced in this paper that relates the regularity of a mapping to subspaces

Characterisations of Ideal Threshold Schemes

We characterise ideal threshold schemes from different approaches. Since the characteristic properties are independent to particular descriptions of threshold schemes all ideal threshold schemes can be examined by new points of view and new results on ideal threshold schemes can be discovered

Lego DNA assembling, a simple in vitro method for constructing DNA molecule

Digestion-ligation based and recombination based methods for constructing recombinant DNA are the basic techniques in molecular biology and thus built one of the foundations for the modern life sciences. Here we describe a new strategy that can radically simplify some of the same task. The lego DNA assembling, based on strand annealing, allows in vitro assembly of multi DNA fragments in one step with precise junctions and excludes the need for any enzyme. As a proof of concept, we rapidly constructed plasmids from 4, 6 and 8 fragments with very high efficiencies (100%). And we found this method a powerful tool for synthetic biology, constructing a partial isoprene biosynthesis pathway (consisting of four genes) in 2 days. We also assembled a customized expression vector to show its modularity

Manipulation of the precursor supply for high-level production of longifolene by metabolically engineered \u3ci\u3eEscherichia coli\u3c/i\u3e

Longifolene is a naturally occurring tricyclic sesquiterpene widely used in many different fields. Up to now, this valuable terpene was mainly manufactured from the high-boiling fraction of certain pine resins. Microbial production can be a promising alternative to the extraction from natural plant sources. Here, we present the metabolic engineering strategy to assemble biosynthetic pathway for longifolene production in Escherichia coli. E. coli was rendered to produce longifolene by heterologously expressing a codon optimized longifolene synthase from Picea abies. Augmentation of the metabolic flux to farnesyl pyrophosphate (FPP) by different FPP synthases conferred a 1.8-fold increase in longifolene production. An additional enhancement of longifolene production (up to 2.64 mg/L) was achieved by introducing an exogenous mevalonate pathway. Under fed-batch conditions, the best-performing strain was able to produce 382 mg/L of longifolene in a 5 L bioreactor. These results demonstrated the feasibility of producing longifolene by microbial fermentation and could serve as the basis for the construction of more robust strains in the future

Influence of eight rootstocks on fruit quality of Morus multicaulis cv. ‘Zijing’ and the comprehensive evaluation of fruit quality traits

Mulberry (Morus L.) has become an important crop throughout the world due to its fruits have been industrially exploited for various commercially valuable products. Many studies on mulberry related to genetic diversity, fruit quality, and breeding programs have been carried out, but little information on mulberry rootstocks is available, especially the possibility of applying grafting to improve the fruit quality. Here, we evaluated the effects of 8 different rootstocks on the fruit quality of ‘Zijing’ mulberry. Twelve fruit quality traits were extremely different except for the fruit shape index (FSI). ‘Zijing’ on ‘Zheza 2’ had the highest fruit weight (FW) and size, as well as titratable acidity (TA), but lower levels of other compounds content except the total soluble solids content (TSS) were detected. ‘Yuesang 51’ exhibited the highest soluble sugar content (SSC), reducing sugar content (RSC), SSC/TA ratio, anthocyanin content (AC) and the lower TA. In contrast, the lowest TSS, SSC and RSC were shown in ‘Guisang 5’. Moreover, ‘Guisang 12’ exhibited the highest TSS and soluble protein content (SPC). The highest vitamin C content (VC) was observed in ‘Guisang 6’. ‘Tang 10 × Lun109’, Zhenzhubai seedlings, ‘Yuesang 11’ together with ‘Yuesang 51’ had the lowest and similar levels of TA. Most importantly, these fruit quality traits were evaluated by principal component analysis (PCA), and ‘Yuesang 51’ with good comprehensive fruit quality was screened out, followed by ‘Guisangyou 12’. Overall, these results contribute to evaluating the roles of different rootstocks on improving fruit quality of mulberry